lecture 2 - Descriptive Statistics

What is the mean?

The arithmetic average; sum of all values divided by the number of values.

When is the mean useful?

When all values are relevant and equally important.

What is the median?

The middle value when data is sorted in order.

When is the median useful?

When the data has extreme values (outliers) or is skewed.

What is the mode?

The value that occurs most frequently in a dataset.

When is the mode useful?

When identifying the most common value (especially for categorical data).

How do you find the median for an even number of values?

Take the average of the two middle numbers after sorting the data.

What is the weighted mean?

A mean that accounts for different weights (frequencies) for each value.

How do you calculate a weighted mean?

Multiply each value by its weight, sum the results, then divide by the total of the weights.

What is the geometric mean?

The nth root of the product of n values, often used for growth rates.

How do you calculate geometric mean growth rate?

Multiply growth factors (1 + rate), take the nth root, then subtract 1.

What are percentiles?

Values that divide data into 100 equal parts.

What are quartiles?

Values that divide data into 4 equal parts (Q1 = 25%, Q2 = median, Q3 = 75%).

What is the interquartile range (IQR)?

Difference between the third and first quartile (Q3 - Q1); measures middle 50% spread.

What is the range in statistics?

Largest value minus the smallest value in the dataset.

What is variance?

A measure of how far values are from the mean on average (uses squared differences).

What is standard deviation?

The square root of the variance; measures typical distance from the mean.

What is the coefficient of variation (CV)?

A measure of relative variation: standard deviation divided by the mean (expressed as %).

Why use coefficient of variation?

To compare variability across datasets with different units or means.

What is Chebyshev’s Theorem?

States that a minimum percentage of data falls within k standard deviations from the mean for any distribution.

What does the Empirical Rule state?

In a normal distribution: 68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD.

What is a z-score?

A standardized value showing how many standard deviations a value is from the mean.

What is the formula for a z-score?

(Value - Mean) ÷ Standard Deviation.

What does a high z-score indicate?

A value far above the mean.

What is a negative z-score?

A value below the mean.

What does covariance measure?

The direction of the relationship between two variables.

What does correlation measure?

The strength and direction of a linear relationship between two variables (between -1 and +1).